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/* mpfr_acosh -- inverse hyperbolic cosine
Copyright 2001, 2002, 2003, 2004, 2005 Free Software Foundation.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Place, Fifth Floor, Boston,
MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* The computation of acosh is done by *
* acosh= ln(x + sqrt(x^2-1)) */
int
mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
{
MPFR_SAVE_EXPO_DECL (expo);
int inexact;
int comp;
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
/* Deal with special cases */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
/* Nan, or zero or -Inf */
if (MPFR_IS_INF (x) && MPFR_IS_POS (x))
{
MPFR_SET_INF (y);
MPFR_SET_POS (y);
MPFR_RET (0);
}
else /* Nan, or zero or -Inf */
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
}
comp = mpfr_cmp_ui (x, 1);
if (MPFR_UNLIKELY (comp < 0))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_UNLIKELY (comp == 0))
{
MPFR_SET_ZERO (y); /* acosh(1) = 0 */
MPFR_SET_POS (y);
MPFR_RET (0);
}
MPFR_SAVE_EXPO_MARK (expo);
/* General case */
{
/* Declaration of the intermediary variables */
mpfr_t t;
/* Declaration of the size variables */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
mp_exp_t err, exp_te, exp_ti; /* Precision of error */
MPFR_ZIV_DECL (loop);
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
/* initialization of intermediary variables */
mpfr_init2 (t, Nt);
/* First computation of acosh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute acosh */
mpfr_mul (t, x, x, GMP_RNDD); /* x^2 */
exp_te = MPFR_GET_EXP (t);
mpfr_sub_ui (t, t, 1, GMP_RNDD); /* x^2-1 */
exp_ti = MPFR_GET_EXP (t);
mpfr_sqrt (t, t, GMP_RNDN); /* sqrt(x^2-1) */
mpfr_add (t, t, x, GMP_RNDN); /* sqrt(x^2-1)+x */
mpfr_log (t, t, GMP_RNDN); /* ln(sqrt(x^2-1)+x)*/
/* error estimate -- see algorithms.tex */
err = 2 + MAX (1, exp_te - exp_ti) - MPFR_GET_EXP(t);
/* error is bounded by 1/2 + 2^err <= 2^(1+max(-1,err)) */
err = 1 + MAX (-1, err);
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - err, Ny, rnd_mode)))
break;
/* reactualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
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